Pol
xA formal indeterminate (formal variable) which may be used to construct polynomials or rational functions as algebraic objects.
xnA formal indeterminate (formal variable) which may be used to construct polynomials or rational functions as algebraic objects, distinguished by an index n.
(x1,x2,x3)Three formal indeterminates.
x1=0andx1=x2A formal indeterminate is not the same thing as an expression-level variable; it is a concrete mathematical object, and in particular an object distinct from any number and from any other indeterminate.
xn−xn=0xn=0andxn0=xnxn=1Indeterminates of this type generates algebras with ordinary numbers as coefficients. They are not suitable for working in rings with different Zero and One elements.
x1x2=x2x1Indeterminates of this type commutes with numbers and with other indeterminates of the same kind.
Input: Where(Equal(Sum(Pol(i), For(i, 1, m))**n, Sum((Factorial(n) / Product(Factorial(Item(k, i)), For(i, 1, m)) * Product(Pol(i)**Item(k, i), For(i, 1, m))), ForElement(k, S))), Def(S, Set(k, ForElement(k, CartesianPower(Range(0,n), m)), Equal(Sum(Item(k, i), For(i, 1, m)), n)))) (i=1∑mxi)n=k∈S∑∏i=1m(ki)!n!i=1∏mxiki where S={k:k∈{0,1,…,n}mandi=1∑mki=n}The multinomial theorem for formal indeterminates.
Last updated: 2020-03-06 00:22:16